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y^'= x/(1+x^2)

解答

y^{^{'}} = \frac{x}{1 + x ^{2}}

解答

y = \frac{1}{2} ln (1 + x^{2}) + c_{1}

求解步骤

y^{'} (x) = \frac{x}{1 + x ^{2}}

若

f^{^{'}} (x) = g (x)

则

f (x) = \int g (x) d x

y = \int \frac{x}{1 + x ^{2}} d x

\int \frac{x}{1 + x ^{2}} d x = \frac{1}{2} ln (1 + x^{2}) + c_{1}

y = \frac{1}{2} ln (1 + x^{2}) + c_{1}

作图

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